Finite Group Databasebeta

← #26133352

Subgroups — #26133352

Order 12032.

554 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093967C211yesmaximal, characteristic
2C2×C4×D376C211yesmaximal, characteristic
3C2×#15688927C211yesmaximal, characteristic, complemented
4C2×#15688923C211yesmaximal, characteristic
5#20241479C211yesmaximal, characteristic, complemented
6#20241466C211yesmaximal, characteristic, complemented
7C47×#1969C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×C4×D188—21no—
10C2×#13093967—22no—
11C2×#13093967—22no—
12C2×#13093967C414yescomplemented
13C22×C47⋊C16C2211yescharacteristic
14C22×C47⋊C16C2211yescharacteristic
15C4×D376—22no—
16C4×D376—22no—
17C2×#13093958C2211yescharacteristic
18C2×#13093946—21no—
19#15688927—22no—
20#15688923—22no—
21C22×Q16×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#103×C47—21no—
24C2×C4×C8×C47C2211yescharacteristic
25C47×#391—21no—
26C22×D188—21no—
27C22×C4×D47—41no—
28C2×D376—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376C2×C412yes—
32C2×D376D412yes—
33C2×D376D412yes—
34C4×D188—24no—
35C4×D188—42no—
36C2×C4⋊Dic47—21no—
37C2×(C2×D47)⋊C4—41no—
38#13093967—28no—
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41C2×C47⋊C16—21no—
42C2×C47⋊C16—21no—
43C2×C47⋊C16—21no—
44C2×C47⋊C16C2×C412yescomplemented
45#13093958—21no—
46#13093958D412yes—
47#13093946—24no—
48C22×Q8×C47—21no—
49C2×Q16×C47—21no—
50C2×Q16×C47—21no—
51C2×Q16×C47—21no—
52C2×Q16×C47—21no—
53C2×Q16×C47—21no—
54C2×Q16×C47C2×C412yescomplemented
55C22×C8×C47D411yescharacteristic
56C22×C8×C47C2311yescharacteristic
57C2×C4⋊C4×C47—21no—
58C2×C42×C47D411yescharacteristic
59#107×C47—21no—
60#107×C47—21no—
61#103×C47—42no—
62C4×C8×C47—21no—
63C4×C8×C47—21no—
64#95×C47—41no—
65#95×C47—41no—
66C23×D47—41no—
67C2×Q8×C47—22no—
68C2×Q8×C47—41no—
69C2×Q8×C47—41no—
70C2×Q8×C47—41no—
71C2×Q8×C47—41no—
72C2×Q8×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47D811yescharacteristic
76C22×C4×C47D811yescharacteristic
77C22×C4×C47C2×D411yescharacteristic
78C22×Dic47—41no—
79C2×D188—22no—
80C2×D188—22no—
81C2×D188—22no—
82C2×D188—41no—
83C2×D188—41no—
84C2×D188—41no—
85C2×C4×D47—44no—
86C2×C4×D47—82no—
87C2×C4×D47—82no—
88Q16×C47—22no—
89Q16×C47—22no—
90Q16×C47—41no—
91Q16×C47—41no—
92C2×C8×C47—21no—
93C2×C8×C47—21no—
94C2×C8×C47—21no—
95C2×C8×C47C22×C411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47#4111yescharacteristic
100C2×C8×C47#4111yescharacteristic
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C42×C47—21no—
104C42×C47—21no—
105(C2×D47)⋊C4—44no—
106C4⋊Dic47—22no—
107C4⋊Dic47—41no—
108D376—22no—
109D376—22no—
110D376—22no—
111D376C22⋊C414yes—
112C47⋊C16—22no—
113C47⋊C16—41no—
114C23×C47C2×D811yescharacteristic
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—81no—
119C22×D47—81no—
120C22×D47—81no—
121C22×D47—81no—
122Q8×C47—42no—
123Q8×C47—42no—
124Q8×C47—81no—
125Q8×C47—81no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—42no—
132C2×C4×C47—81no—
133C2×C4×C47—81no—
134C2×C4×C47—81no—
135C2×C4×C47—81no—
136C2×C4×C47—81no—
137C2×C4×C47SD3212yescomplemented
138C2×C4×C47C4×D411yescharacteristic
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47#12111yescharacteristic
141C2×C4×C47#13511yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C2×Dic47—42no—
145C2×Dic47—81no—
146C2×Dic47—81no—
147D188—24no—
148D188—42no—
149D188—42no—
150D188—42no—
151C4×D47—88no—
152C8×C47—41no—
153C8×C47C2×C22⋊C411yescharacteristic
154C8×C47C4×D411yescharacteristic
155C8×C47#12111yescharacteristic
156C8×C47#12311yescharacteristic
157#13014—471nomaximal, Sylow
158C22×C47C4×D811yescharacteristic
159C22×C47#44711yescharacteristic
160C22×C47#45911yescharacteristic
161C22×C47C2×SD3211yescharacteristic
162C22×C47#50811yescharacteristic
163C22×C47#50911yescharacteristic
164C22×C47#51011yescharacteristic
165C2×D47—44no—
166C2×D47—82no—
167C2×D47—82no—
168C2×D47—82no—
169C2×D47—82no—
170C2×D47—82no—
171C2×D47—82no—
172C4×C47—22no—
173C4×C47—41no—
174C4×C47—82no—
175C4×C47—161no—
176C4×C47#38611yescharacteristic
177C4×C47#44211yescharacteristic
178C4×C47#44911yescharacteristic
179C4×C47#46311yescharacteristic
180Dic47—82no—
181C22×SD32—471no—
182C2×C4×D8—471no—
183C2×#358—471no—
184C2×#357—471no—
185#1969D4711yescharacteristic, complemented
186#1380—471no—
187#1374—471no—
188C2×C47#187911yescharacteristic
189C2×C47C4×SD3211yescharacteristic
190C2×C47#217511yescharacteristic
191C2×C47#218711yescharacteristic
192C2×C47#218911yescharacteristic
193C2×C47#220811yescharacteristic
194C2×C47#221011yescharacteristic
195D47—84no—
196C22×Q16C2×D4711yescharacteristic
197C22×D8—471no—
198C2×C4×D4—941no—
199C2×SD32—474no—
200C2×SD32—942no—
201C2×SD32—942no—
202C22×C16—471no—
203C22×C16—471no—
204C4×D8—942no—
205C4×D8—942no—
206C2×#107—471no—
207C2×#107C2×D4711yescharacteristic
208C2×#103—21no—
209C2×#102—941no—
210C2×C4×C8C2×D4711yescharacteristic
211#391—21no—
212#358—942no—
213#357—942no—
214C47#1301411yescharacteristic, complemented, Sylow
215C22×Q8—21no—
216C22×D4—941no—
217C23×C4—1881no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16—21no—
223C2×Q16C4×D4712yescomplemented
224C2×D8—472no—
225C2×D8—472no—
226C2×D8—472no—
227C2×D8—941no—
228C2×D8—941no—
229C2×D8—941no—
230C22×C8C22⋊D4711yescharacteristic
231C22×C8C22×D4711yescharacteristic
232C4×D4—944no—
233C4×D4—1882no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—941no—
236C2×C22⋊C4—1881no—
237C2×C42C22⋊D4711yescharacteristic
238SD32—948no—
239C2×C16—472no—
240C2×C16—941no—
241C2×C16—941no—
242C2×C16—941no—
243C2×C16—941no—
244C2×C16—941no—
245#107—21no—
246#107—21no—
247#107—472no—
248#107—941no—
249#103—42no—
250#102—944no—
251C4×C8—21no—
252C4×C8—21no—
253#95—41no—
254#95—41no—
255C24—1881no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—942no—
263C2×D4—942no—
264C2×D4—942no—
265C2×D4—1881no—
266C2×D4—1881no—
267C2×D4—1881no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—3762no—
271C22×C4—3762no—
272C22×C4—1884no—
273C22×C4—1881no—
274C22×C4#1062533411yescharacteristic
275C22×C4#1062533411yescharacteristic
276C22×C4C2×C22⋊D4711yescharacteristic
277Q16—22no—
278Q16—22no—
279Q16—41no—
280Q16—41no—
281D8—474no—
282D8—942no—
283D8—942no—
284D8—942no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8C2×C4×D4711yescharacteristic
289C2×C8#1062535011yescharacteristic
290C2×C8D4×D4711yescharacteristic
291C2×C8D4×D4711yescharacteristic
292C2×C8D4×D4711yescharacteristic
293C2×C8#1062535211yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—942no—
297C4⋊C4—1881no—
298C22⋊C4—1884no—
299C42—21no—
300C42—21no—
301C16—942no—
302C16—1881no—
303C23—3761no—
304C23—3761no—
305C23—3761no—
306C23—3761no—
307C23—1882no—
308C23—1882no—
309C23—1882no—
310C23C2×#1062533411yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—81no—
314Q8—81no—
315D4—944no—
316D4—1882no—
317D4—1882no—
318D4—1882no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—3768no—
331C2×C4—3761no—
332C2×C4—3761no—
333C2×C4—1882no—
334C2×C4#1309396712yescomplemented
335C2×C4C4×C22⋊D4711yescharacteristic
336C2×C4#1309399211yescharacteristic
337C2×C4#1309399511yescharacteristic
338C2×C4#1309404411yescharacteristic
339C2×C4#1309404911yescharacteristic
340C2×C4#1309405011yescharacteristic
341C8—41no—
342C8C22⋊C4×D4711yescharacteristic
343C8(C22⋊D47)⋊C411yescharacteristic
344C8#1309399711yescharacteristic
345C8#1309400611yescharacteristic
346C22—3762no—
347C22—3762no—
348C22—3762no—
349C22—3762no—
350C22—3762no—
351C22—3762no—
352C22—1884no—
353C22C4×#1062533411yescharacteristic
354C22#1568925611yescharacteristic
355C22#1568931511yescharacteristic
356C22C2×#1309396711yescharacteristic
357C22#1568955311yescharacteristic
358C22#1568955811yescharacteristic
359C22#1568956411yescharacteristic
360C4—22no—
361C4—41no—
362C4—82no—
363C4—161no—
364C4—3762no—
365C4#1568899911yescharacteristic
366C4#1568923311yescharacteristic
367C4#1568926611yescharacteristic
368C4#1568933511yescharacteristic
369C2—3764no—
370C2#2024373911yescharacteristic
371C2C4×#1309396711yescharacteristic
372C2#2024525011yescharacteristic
373C2#2024531611yescharacteristic
374C2#2024532611yescharacteristic
375C2#2024543011yescharacteristic
376C2#2024544011yescharacteristic
subgroupG/H
centerC23C2×#10625334
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1969C2
socleC23×C47C2×D8
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenter#1969D47
hypocenterC47#13014
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#15688927C2semidirect
5. #20241479C2semidirect
6. #20241466C2semidirect
7. C47×#1969C2semidirect
12. C2×#13093967C4semidirect
44. C2×C47⋊C16C2×C4semidirect
54. C2×Q16×C47C2×C4semidirect
137. C2×C4×C47SD32semidirect
185. #1969D47semidirect
214. C47#13014semidirect
223. C2×Q16C4×D47semidirect
334. C2×C4#13093967semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130939672
C2×C4×D3762
C2×#156889272
C2×#156889232
#202414792
#202414662
C47×#19692
#1301447